Algebra: Measurement
One of the equal sides of an isosceles triangle is 3 m less than twice its base. The perimeter is 44 m. Find the lengths of the sides.
the angles sum to 180.
So, if the base is x, each of the other two sides is 2x-3.
SO, now you have to find x when
x + 2x-3 + 2x-3 = 44
Having found x, you can now determine the lengths of the sides.
To solve this problem, we can use the given information and set up equations to represent the relationships between the sides of the triangle.
Let's denote the length of the base of the isosceles triangle as 'x' meters. Since one of the equal sides is 3 meters less than twice the base, the length of each of these equal sides can be represented as (2x - 3) meters.
Now, we can use the concept of perimeter, which is the sum of all the sides of the triangle, to set up an equation:
Perimeter = length of the base + length of equal side + length of equal side
Since we know the perimeter of the triangle is 44 meters, we can substitute the values:
44 = x + (2x - 3) + (2x - 3)
Simplifying the equation:
44 = x + 2x - 3 + 2x - 3
Combining like terms:
44 = 5x - 6
Add 6 to both sides:
44 + 6 = 5x - 6 + 6
50 = 5x
Divide both sides by 5:
50/5 = 5x/5
10 = x
Therefore, the base of the isosceles triangle is 10 meters.
To find the lengths of the equal sides, we can substitute the value of 'x' back into the expression we derived earlier:
Length of equal side = 2x - 3
Length of equal side = 2(10) - 3
Length of equal side = 20 - 3
Length of equal side = 17 meters
So, the lengths of the sides of the isosceles triangle are: base = 10 meters, and equal sides = 17 meters.